INEXPERIENCED AND UNFAMILIAR LJ31 FLT CREW STRUGGLE TO COMPLY WITH ATC CLRNCS ON VMC ARR TO LGA.

Narrative

UPON ARR IN RDU; I WAS INFORMED THE PAX NOW WANTED TO GO TO LGA. SO I MADE THE ARRANGEMENTS; FILED; GOT RESERVATIONS IN AND OUT OF LGA AND CHKED WX AND NOTAMS AND WE DEPARTED. I HADN'T REVIEWED THE LGA CHARTS AS WE NEEDED TO GET UNDERWAY. UPON DSCNT INTO NEW YORK I REPEATEDLY HEARD APCH GIVING ACFT INSTRUCTIONS TO 'FOLLOW THE HUDSON.' ATIS SAID LGA WAS LNDG RWY 22; I BELIEVE IT IS. I KNEW I DIDN'T KNOW WHERE THE HUDSON WAS; SO I ASKED THE COPLT TO FIND THE HUDSON DEPICTED ON ANY OF THE APCH PLATES ARRS OR CHARTS. HE WAS UNABLE TO DO SO; SO I TOLD HIM WE WOULD NEED TO GET CLARIFICATION IF THEY ASSIGNED US THE SAME INSTRUCTIONS. HE FOUND THE RIVER VISUAL TO RWY 13; BUT WAS UNABLE TO FIND ANY MARKINGS ON THE ARR THAT STATED WHICH RIVER WAS THE HUDSON; AS THE RIVER SPLIT TO THE E AND W OF MANHATTAN. THE RIVER ON THE E LEADS TO LGA BUT THE RIVER ON THE W IS WHAT YOU FOLLOW FOR THE RIVER VISUAL TO RWY 13L. AS WE WEREN'T LNDG RWY 13; THIS DIDN'T HELP CLARIFY OUR SITUATION IF WE WERE ASSIGNED TO FOLLOW THE HUDSON. WE CONTINUED ALONG OUR RTE THAT WE WERE ASSIGNED AND WERE GIVEN INSTRUCTIONS TO DSND TO 4000 FT AND FOLLOW THE HUDSON. THE COPLT DIDN'T ASK FOR CLARIFICATION BUT JUST ACCEPTED THE INSTRUCTIONS. I TOLD HIM TO FIND ME THE HUDSON OR GET CLARIFICATION NOW; AS I DIDN'T WANT HIM TO ACCEPT THEM WITHOUT CLARIFICATION. WHILE WE WERE WORKING ON FIGURING OUT WHICH RIVER WAS THE HUDSON; AS THE APCH FREQ WAS PRETTY BUSY; AS WE WERE WORKING ON THIS WE WERE TOLD TO SLOW TO 210 KTS. I BEGAN TO SLOW. AS WE APCHED 4000 FT; I NOTICED THE AUTOPLT WASN'T SLOWING. AS IT HIT 4000 FT; I NOTICED IT HADN'T LEVELED OFF. I KICKED OFF THE AUTOPLT AND LEVELED OFF AT 4000 FT. AS I DID; I NOTICED THE ALT ALERTER WAS SET TO 2100 FT. I ASKED WHEN WE GOT THAT ASSIGNMENT AS I NEVER HEARD IT. I ASSUMED HE MISTOOK 210 KTS FOR 2100 FT. HE GOT A CALL TO APCH TO ASK THEM WHAT WE WERE CLRED TO AND THEY SAID 4000 FT AND IT LOOKED LIKE WE WERE E OF WHERE WE SHOULD BE. I RESPONDED WITH WE WERE TRYING TO GET CLARIFICATION. I TOOK AN IMMEDIATE TURN TO THE W EDGE OF THE HUDSON RIVER ON THE W SIDE OF MANHATTAN AND CONTINUED UNTIL ABOUT 5 MI OUT ON FINAL. WE WERE TOLD BY APCH TO 'CONTACT TWR 118.57.' WE WENT TO TWR AND WERE INFORMED IT WAS WESTCHESTER TWR. THE COPLT FOUND ON THE CHART TWR WAS 118.7 NOT 118.57 ALTHOUGH I KNOW THAT'S WHAT WE WERE ASSIGNED AND READ BACK. WE SWITCHED TO 118.7 ABOUT A 3 MI FINAL TO HEAR LGA TWR CALLING US AND SOUNDING A LITTLE ANNOYED. I EXPLAINED WE WERE GIVEN WESTCHESTER TWR AND HE REPLIED; 'YOU'RE LNDG AT LGA AREN'T YOU?' -- SOUNDING EVEN MORE ANNOYED. SO I LET IT GO. WE LANDED WITHOUT INCIDENT AND THE REST OF THE TRIP WAS UNEVENTFUL. AFTER LNDG; I REVIEWED THE PLATES MYSELF TO SEE THAT THE RIVER VISUAL TO RWY 13 NOT ONLY SHOWS HUDSON RIVER IN THE RIVER AS WELL AS IN THE TEXTUAL DESCRIPTION LABELING THE HUDSON. MY QUESTION IS; IF THEY USE THIS ARR FOR MORE THAN 1 RWY; WHY IS IT LABELED RIVER VISUAL TO RWY 13? WHY DON'T THEY REFER TO FOLLOWING THE RIVER VISUAL NOT FOLLOWING THE HUDSON FOR PEOPLE WHO DON'T FLY IN THERE EVERYDAY. WE MADE A COUPLE ERRORS WHICH UNFORTUNATELY COMPOUNDED THEMSELVES. I SHOULD HAVE MADE TIME TO REVIEW THE PLATES MYSELF PRIOR TO DEP. THE ALT SET TO 2100 FT BY THE COPLT AND HIS INABILITY TO FIND THE WRITING OF THE 'HUDSON RIVER.'